Predicting Proton-Air Cross Sections ats∼30TeVUsing Accelerator and Cosmic Ray Data

We use the high-energy predictions of a QCD-inspired parametrization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, along with Glauber theory, to predict proton-air cross sections at energies near $\sqrt{s}\approx 30\mathrm{TeV}$. The parametrization of the proton-proton cross section incorporates analyticity and unitarity and demands that the asymptotic proton is a black disk of soft partons. By comparing with the $p$-air cosmic ray measurements, our analysis results in a constraint on the inclusive particle production cross section.